Related papers: Sally modules of ${\mathfrak m}$-primary ideals in…

Let $I$ denote an ideal of a local Gorenstein ring $(R, \mathfrak m)$. Then we show that the local cohomology module $H^c_I(R), c = \height I,$ is indecomposable if and only if $V(I_d)$ is connected in codimension one. Here $I_d$ denotes…

Let $\mathfrak{a}$ be an ideal of a commutative noetherian ring $R$ and $M$ an $R$-module with Cosupport in $\mathrm{V}(\mathfrak{a})$. We show that $M$ is $\mathfrak{a}$-coartinian if and only if $\mathrm{Ext}_{R}^{i}(R/\mathfrak{a},M)$ is…

Let $A$ be a non Gorenstein Cohen Macaulay ring of dimension $d\geq 1$, $I$ an ideal of $A$, and suppose $\omega_A$ is a canonical $A$-module. Set $$r(I,\omega_A) = \bigcup_{n \geq 0} (I^{n+1} \omega_A : I^{n} \omega_A) \subseteq A .$$ We…

Let $R$ be a commutative Noetherian ring, $M$ a finitely generated $R$-module and $n$ be a non-negative integer. In this article, it is shown that there is a finitely generated submodule $N_i$ of $H_{\frak a}^i(M)$ such that $\dim{\rm Supp…

In this paper we prove the following generalization of a result of Hartshorne: Let $(S,\n)$ be a regular local ring of dimension $4$. Assume that $x,y,u,v$ is a regular system of parameters for $S$ and $a:=xu+yv$. Then for each finitely…

Let $(R,m)$ be a local Noetherian ring, let $I\subset R$ be any ideal and let $M$ be a finitely generated $R$-module. In 1990 Craig Huneke conjectured that the local cohomology modules $H^i_I(M)$ have finitely many associated primes for all…

Let $A$ be a commutative noetherian ring, let $\mathfrak a$ be an ideal of $A$ and let $n$ be a non-negative integer. In this paper, we study $\mathcal{S}_{n}(\mathfrak{a})$, a certain class of $A$-modules and we find some sufficient…

We characterise ideals in two-dimensional regular local rings that arise as ideals of maximal minors of indecomposable integrally closed modules of rank three.

Let $\frak a$ be an ideal of a commutative noetherian ring $R$ with unity and $M$ an $R$-module supported at $\V(\fa)$. Let $n$ be the supermum of the integers $i$ for which $H^{\fa}_i(M)\neq 0$. We show that $M$ is $\fa$-cofinite if and…

This paper purposes to characterize Noetherian local rings $(R, \mathfrak{m})$ such that the Chern numbers of certain $\mathfrak{m}$-primary ideals in $R$ bounded above or range among only finitely many values. Consequently, we characterize…

Let $(R,\mathfrak{m})$ be a commutative Noetherian local ring, and suppose $R$ is Cohen-Macaulay with canonical module $\omega_R$. We develop new tools for analyzing questions involving annihilators of several homologically defined objects.…

For a Cohen-Macaulay local ring $(R,\mathfrak{m})$ with canonical module, we study how relations between $\text{index}(R)$ and $\text{g}\ell\ell(R)$ and between $\text{index}(R)$ and $e(R)$ are preserved when factoring out regular sequences…

Let T be a commutative Noetherian local ring of dimension at least two and R=T[x_1,...,x_n] a polynomial ring in n variables over T. Consider R as a graded ring with deg T = 0 and deg x_i = 1 for all i. Let I=R_+ and f a homogeneous…

The j-multiplicity is an invariant that can be defined for any ideal in a Noetherian local ring $(R, m)$. It is equal to the Hilbert-Samuel multiplicity if the ideal is $m$-primary. In this paper we explore the computability of the…

We compute the local cohomology modules H_Y^(X,O_X) in the case when X is the complex vector space of n x n symmetric, respectively skew-symmetric matrices, and Y is the closure of the GL-orbit consisting of matrices of any fixed rank, for…

This paper is concerned about the relation between local cohomology modules defined by a pair of ideals and Serre classes of R-modules, as a generalization of results of J. Azami, R. Naghipour and B. Vakili (2009) and M. Asgharzadeh and…

This work concerns the stable module category of a finite group over a field of characteristic dividing the group order. The minimal localising tensor ideals correspond to the non-maximal homogeneous prime ideals in the cohomology ring of…

Let $(R, \mathfrak m)$ be a Cohen-Macaulay local ring of dimension $d \geq 2,$ and $I$ an $\mathfrak m$-primary ideal of $R.$ Denote $r_{J}(I)$ as the reduction number of $I$ with respect to a minimal reduction $J$ of $I,$ and $\rho(I)$ as…

A well-known result of K\"{o}the and Cohen-Kaplansky states that a commutative ring $R$ has the property that every $R$-module is a direct sum of cyclic modules if and only if $R$ is an Artinian principal ideal ring. This motivated us to…

A commutative ring $R$ is stable provided every ideal of $R$ containing a nonzerodivisor is projective as a module over its ring of endomorphisms. The class of stable rings includes the one-dimensional local Cohen-Macaulay rings of…